Controlled multi-photon subtraction with cascaded Rydberg superatoms as single-photon absorbers.

The preparation of light pulses with well-defined quantum properties requires precise control at the individual photon level. Here, we demonstrate exact and controlled multi-photon subtraction from incoming light pulses. We employ a cascaded system of tightly confined cold atom ensembles with strong, collectively enhanced coupling of photons to Rydberg states. The excitation blockade resulting from interactions between Rydberg atoms limits photon absorption to one per ensemble and rapid dephasing of the collective excitation suppresses stimulated re-emission of the photon. We experimentally demonstrate subtraction with up to three absorbers. Furthermore, we present a thorough theoretical analysis of our scheme where we identify weak Raman decay of the long-lived Rydberg state as the main source of infidelity in the subtracted photon number and investigate the performance of the multi-photon subtractor for increasing absorber numbers in the presence of Raman decay.

The low-energy Goldstone mode in a trapped dipolar supersolid.

A supersolid is a counter-intuitive state of matter that combines the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid1,2. Since the first prediction3 in the 1950s, experimental efforts to realize this state have focused mainly on helium, in which supersolidity remains unobserved4. Recently, supersolidity has also been studied in ultracold quantum gases, and some of its defining properties have been induced in spin-orbit-coupled Bose-Einstein condensates (BECs)5,6 and BECs coupled to two crossed optical cavities7,8. However, no propagating phonon modes have been observed in either system. Recently, two of the three hallmark properties of a supersolid-periodic density modulation and simultaneous global phase coherence-have been observed in arrays of dipolar quantum droplets9-11, where the crystallization happens in a self-organized manner owing to intrinsic interactions. Here we directly observe the low-energy Goldstone mode, revealing the phase rigidity of the system and thus proving that these droplet arrays are truly supersolid. The dynamics of this mode is reminiscent of the effect of second sound in other superfluid systems12,13 and features an out-of-phase oscillation of the crystal array and the superfluid density. This mode exists only as a result of the phase rigidity of the experimentally realized state, and therefore confirms the superfluidity of the supersolid.

Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms.

The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.

Observation of Three-Body Correlations for Photons Coupled to a Rydberg Superatom.

We report on the experimental observation of nontrivial three-photon correlations imprinted onto initially uncorrelated photons through an interaction with a single Rydberg superatom. Exploiting the Rydberg blockade mechanism, we turn a cold atomic cloud into a single effective emitter with collectively enhanced coupling to a focused photonic mode which gives rise to clear signatures in the connected part of the three-body correlation function of the outgoing photons. We show that our results are in good agreement with a quantitative model for a single, strongly coupled Rydberg superatom. Furthermore, we present an idealized but exactly solvable model of a single two-level system coupled to a photonic mode, which allows for an interpretation of our experimental observations in terms of bound states and scattering states.

Quasiparticles in Quantum Spin Chains with Long-Range Interactions.

We study quasiparticle excitations for quantum spin chains with long-range interactions using variational matrix product state techniques. It is confirmed that the local quasiparticle ansatz is able to capture those excitations very accurately, even when the correlation length becomes very large and in the case of topological nontrivial excitation such as spinons. It is demonstrated that the breaking of the Lieb-Robinson bound follows from the appearance of cusps in the dispersion relation, and evidence is given for a crossover between different quasiparticles as the long-range interactions are tuned.

Emergent Universal Dynamics for an Atomic Cloud Coupled to an Optical Waveguide.

We study the dynamics of a single collective excitation in a cold ensemble of atoms coupled to a one-dimensional waveguide. The coupling between the atoms and the photonic modes provides a coherent and a dissipative dynamics for this collective excitation. While the dissipative part accounts for the collectively enhanced and directed emission of photons, we find a remarkable universal dynamics for increasing atom numbers exhibiting several revivals under the coherent part. While this phenomenon provides a limit on the intrinsic dephasing for such a collective excitation, a setup is presented where the universal dynamics can be explored.

Accurate Mapping of Multilevel Rydberg Atoms on Interacting Spin-1/2 Particles for the Quantum Simulation of Ising Models.

We study a system of atoms that are laser driven to nD_{3/2} Rydberg states and assess how accurately they can be mapped onto spin-1/2 particles for the quantum simulation of anisotropic Ising magnets. Using nonperturbative calculations of the pair potentials between two atoms in the presence of electric and magnetic fields, we emphasize the importance of a careful selection of experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We benchmark these theoretical observations against experiments using two atoms. Finally, we show that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1/2 Ising models in systems with up to 49 spins, for which numerical simulations become intractable.

Full Counting Statistics for Interacting Fermions with Determinantal Quantum Monte Carlo Simulations.

We present a method for computing the full probability distribution function of quadratic observables such as particle number or magnetization for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo calculations. Especially in cold atom experiments with single-site resolution, such a full counting statistics can be obtained from repeated projective measurements. We demonstrate that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find excellent agreement with recent experimental results. We show that current experiments are capable of probing the difference between the Hubbard model and the limiting Heisenberg model.

Three-Body Interaction of Rydberg Slow-Light Polaritons.

We study a system of three photons in an atomic medium coupled to Rydberg states near the conditions of electromagnetically induced transparency. Based on the analytical analysis of the microscopic set of equations in the far-detuned regime, the effective three-body interaction for these Rydberg polaritons is derived. For slow light polaritons, we find a strong three-body repulsion with the remarkable property that three polaritons can become essentially noninteracting at short distances. This analysis allows us to derive the influence of the three-body repulsion on bound states and correlation functions of photons propagating through a one-dimensional atomic cloud.

Role of quantum fluctuations in the hexatic phase of cold polar molecules.

Two-dimensional crystals melt via an intermediate hexatic phase, which is characterized by an anomalous scaling of spatial and orientational correlation functions and the absence of an attraction between dislocations. We propose a protocol to study the effect of quantum fluctuations on the nature of this phase with a model system of strongly correlated ultracold polar molecules. Dislocations can be located in experiment from local energy differences which induce internal stark shifts in the molecules. We present a criterion to identify the hexatic phase from the statistics of the end points of topological defect strings and find a hexatic phase, which is dominated by quantum fluctuations, between the crystal and superfluid phases.

Coupling a single electron to a Bose-Einstein condensate.

The coupling of electrons to matter lies at the heart of our understanding of material properties such as electrical conductivity. Electron-phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, which forms the basis for Bardeen-Cooper-Schrieffer superconductivity. Here we study the interaction of a single localized electron with a Bose-Einstein condensate and show that the electron can excite phonons and eventually trigger a collective oscillation of the whole condensate. We find that the coupling is surprisingly strong compared to that of ionic impurities, owing to the more favourable mass ratio. The electron is held in place by a single charged ionic core, forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size of up to eight micrometres, comparable to the dimensions of the condensate. In such a state, corresponding to a principal quantum number of n = 202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects caused by the electron exploring the outer regions of the condensate. We anticipate future experiments on electron orbital imaging, the investigation of phonon-mediated coupling of single electrons, and applications in quantum optics.

Driving dipolar fermions into the quantum Hall regime by spin-flip induced insertion of angular momentum.

A new method to drive a system of neutral dipolar fermions into the lowest Landau level regime is proposed. By employing adiabatic spin-flip processes in combination with a diabatic transfer, the fermions are pumped to higher orbital angular momentum states in a repeated scheme that allows for the precise control over the final angular momentum. A simple analytical model is derived to quantify the transfer and compare the approach to rapidly rotating systems. Numerical simulations of the transfer process have been performed for small, interacting systems.

Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields.

We study the interplay of photons interacting with an artificial atom in the presence of a controlled dephasing. Such artificial atoms consisting of several independent scatterers can exhibit remarkable properties superior to single atoms with a prominent example being a superatom based on Rydberg blockade. We demonstrate that the induced dephasing allows for the controlled absorption of a single photon from an arbitrary incoming probe field. This unique tool in photon-matter interaction opens a way for building novel quantum devices, and several potential applications such as a single photon transistor, high fidelity n-photon counters, or the creation of nonclassical states of light by photon subtraction are presented.

Microscopic derivation of Hubbard parameters for cold atomic gases.

We study the exact solution for two atomic particles in an optical lattice interacting via a Feshbach resonance. The analysis includes the influence of all higher bands, as well as the proper renormalization of molecular energy in the closed channel. This exact solution allows for the precise determination of the parameters in the Hubbard model and the two-particle bound state energy. We identify the regime, where a single band Hubbard model fails to describe the scattering properties of the atoms as well as the bound states energies.

Collective many-body interaction in Rydberg dressed atoms.

We present a method to control the shape and character of the interaction potential between cold atomic gases by weakly dressing the atomic ground state with a Rydberg level. For increasing particle densities, a crossover takes place from a two-particle interaction into a collective many-body interaction, where the dipole-dipole or van der Waals blockade phenomenon between the Rydberg levels plays a dominant role. We study the influence of these collective interaction potentials on a Bose-Einstein condensate and present the optimal parameters for its experimental detection.

Two-stage melting in systems of strongly interacting Rydberg atoms.

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low-energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.

Quantum critical behavior in strongly interacting Rydberg gases.

We study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum phase transition. We derive the critical theory for the quantum phase transition and show that it describes the properties of the driven Rydberg system in the saturated regime. We find that the suppression of Rydberg excitations known as blockade phenomena exhibits an algebraic scaling law with a universal exponent.